I gave Graz'zt a couple of more thoughts... this is what I got...
Graz'zt can easily be behind everything, but I think most players would just feel cheated. I think it is important not to have him *plop* out of nowhere near the end of the campaign, like Adimarchus in "The Shackled City". Or imagine killing Orcus at level 30, only to find out Grazzt was behind it... rather anticlimatic.
Thus, I think a plot where the players actually fight against Graz'zt might be better. They only do that, because he wants them to, of course!
Here is my idea:
To finally get rid of Orcus and Demogorgon (three Demon Lords are more than enough for my players attention span, the rest will be ignored or just used as lesser allies of one of the big three) Graz'zt is willing to sacrifice Azzagrat. He sets up powerful mortal heroes to invade his realm and get rid of him while at the same time tricking Orcus and Demogorgon into an alliance to destroy him.
The mortals will find his realm rather easy to invade, only to be surprised by the attack of Orcus and Demogorgons combined forces. The demon host will attack without mercy and control, a huge three way battle starts, most likely, there will be no winner.
Graz'zt has long before evacuated most of his forces into the Elemental Maelstrom, where where he was able to usurp the power of the Efreeti Sultan and the Titans (The Forgotten Realms Campaign Setting puts Thrym, Surtur and other Giant Gods as Titans into the Elemental Maelstrom, where they rule over places like the Glacial Rift...)
With a powerful army of elementals and demons Graz'zt plans to crush the forces of Orcus, Demogorgon with one big stroke.
How to involve the players in this plot?
Heroic Tier: Graz'zt gets their attention. They cross the plans of one of his more prominent mortal followers, maybe more than once. At the end of this tier, this follower of Graz'zt is a well known enemy of the players, and they know he is part of the Cult of Graz'zt. (They do not know a lot about the Dark Prince, yet)
Paragon Tier: Graz'zt sets the players up for greatness. A Caligoristo may possess the fighters sword, making him more powerful and help Graz'zt to controll the group etc.
He helps them, while at the same time setting up the Rakshasa, his most dedicated followers, to bring war and misery to the players homeland in his name.
Epic Tier: By now, the players should know the Cult of Graz'zt, and they should hate him. Time for him to step back. He sets them up for one more big heroic deed (Killing a big dragon or something like that)... to show their power to Demogorgon and Orcus.
After that, the Demonlords plan to use the players as a tool to kill Graz'zt, so they can invade his realm. This goes horribly wrong of course. Finding Azzagrat more or less empty, the savage hordes of Demogorgon and the undead of Orcus will give in to their chaotic nature and attack each other, with the characters trying to sneak their way out of Graz'zt throne room, where they just killed his proxy.
This should be somewhere in the mid epic tier... after that, the players must find a way to break Graz'zt rule over the abyss, before he invades the mortals world.
